Gian Michele Calvi, PhD, is a Full Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at North Carolina State University, USA, in the Department of Civil, Construction, and Environmental Engineering. He is also the founder of the EUCENTRE Foundation for Training and Research in Earthquake Engineering and is currently the Director of the International Association of Earthquake Engineering. Roberto Nascimbene, PhD, is an Associate Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at the University of Pavia, Italy, in the Department of Civil Engineering and Architecture. He is also a National Committee Member of the European UNI/CT 021/SC 03 “Steel Structures” and a member of the Project Team SC8.T5 - Evolution of EN 1998-4 and EN 1998-6 “M/515 Phase 3 or 4.”

• Preface xiAcknowledgments xiiiIntroduction xv1 Appealing shell structures 11.1 Beams and arches . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Plates and vaults . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Rectangular and cylindrical tanks . . . . . . . . . . . . . . . . . . 121.4 Seismic behaviour of tanks . . . . . . . . . . . . . . . . . . . . . 231.5 Field observation of damage to tanks induced by seismic events 381.6 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . 481.7 A simplified description of seismic response of tanks . . . . . . . 571.8 Discussion on existing codes . . . . . . . . . . . . . . . . . . . . . 601.9 Content of the book . . . . . . . . . . . . . . . . . . . . . . . . . 662 Above ground anchored rigid tanks 672.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.2 Circular vertical anchored tanks . . . . . . . . . . . . . . . . . . . 682.2.1 Impulsive pressure component . . . . . . . . . . . . . 712.2.2 Convective pressure component . . . . . . . . . . . . 812.2.3 Effects of vertical component of the seismic action . 89vii2.2.4 Effects of tank inertia . . . . . . . . . . . . . . . . . . 922.2.5 Periods of vibration . . . . . . . . . . . . . . . . . . . 932.2.6 Effects of liquid viscosity . . . . . . . . . . . . . . . . 992.2.7 Effects of inhomogeneous liquids . . . . . . . . . . . 1022.2.8 Convective wave displacement and pressure . . . . . 1112.2.9 Combination of pressures and behavior factor . . . . 1182.2.10 Tank forces and stresses . . . . . . . . . . . . . . . . 1242.2.11 Effects of rocking motion . . . . . . . . . . . . . . . . 1312.3 Rectangular anchored tanks . . . . . . . . . . . . . . . . . . . . . 1362.3.1 Impulsive and convective pressure components . . . 1362.3.2 Periods of vibration . . . . . . . . . . . . . . . . . . . 1412.3.3 Convective wave displacement . . . . . . . . . . . . . 1432.3.4 Tank forces and stresses . . . . . . . . . . . . . . . . 1433 Above ground unanchored rigid tanks 1493.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.2 Vertical cylindrical tanks . . . . . . . . . . . . . . . . . . . . . . . 1533.2.1 Axial membrane stress in shell wall . . . . . . . . . . 1613.2.2 Shell uplift . . . . . . . . . . . . . . . . . . . . . . . . 1653.2.3 Radial membrane stress at base . . . . . . . . . . . . 1673.2.4 Plastic rotation at base . . . . . . . . . . . . . . . . . 1683.3 Rectangular tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1704 Elevated tanks 175viii4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1754.2 Single lumped-mass model . . . . . . . . . . . . . . . . . . . . . . 1824.3 Two uncoupled mass model . . . . . . . . . . . . . . . . . . . . . 1864.4 Two coupled masses model . . . . . . . . . . . . . . . . . . . . . 1905 Flexible tanks 2015.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2015.2 Impulsive pressure component . . . . . . . . . . . . . . . . . . . . 2055.2.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2055.2.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2195.3 Effects of vertical component of the seismic action . . . . . . . 2265.4 Periods of vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 2315.5 Combination of pressures . . . . . . . . . . . . . . . . . . . . . . 2465.6 Tank forces and stresses . . . . . . . . . . . . . . . . . . . . . . . 2555.6.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2575.6.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2705.7 Effects of rocking motion . . . . . . . . . . . . . . . . . . . . . . 2726 Other peculiar principles 2776.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2776.2 Effects of soil–structure interaction . . . . . . . . . . . . . . . . . 2786.3 Flow-dampening devices . . . . . . . . . . . . . . . . . . . . . . . 2886.4 Base-isolation devices . . . . . . . . . . . . . . . . . . . . . . . . 3026.5 Underground rigid tanks . . . . . . . . . . . . . . . . . . . . . . . 313ix6.6 Horizontal tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3176.7 Conical tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3247 General design principles 3337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3337.2 Requirements for steel tanks . . . . . . . . . . . . . . . . . . . . 3347.2.1 Base plate . . . . . . . . . . . . . . . . . . . . . . . . 3357.2.2 Sidewall . . . . . . . . . . . . . . . . . . . . . . . . . . 3397.2.3 Openings . . . . . . . . . . . . . . . . . . . . . . . . . 3487.2.4 Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3537.2.5 Foundation . . . . . . . . . . . . . . . . . . . . . . . . 3627.2.6 Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . 3737.2.7 Buckling limit state . . . . . . . . . . . . . . . . . . . 4067.3 Requirements for concrete tanks . . . . . . . . . . . . . . . . . . 4237.3.1 Serviceability limit state . . . . . . . . . . . . . . . . 4257.3.2 Ultimate limit state . . . . . . . . . . . . . . . . . . . 4357.3.3 Detailing and particular rules . . . . . . . . . . . . . . 436A Dimensionless design charts 463A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463B Codes, Manuals, Recommendations, Guidelines, Reports 471B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Gian Michele Calvi, PhD, is a Full Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at North Carolina State University, USA, in the Department of Civil, Construction, and Environmental Engineering. He is also the founder of the EUCENTRE Foundation for Training and Research in Earthquake Engineering and is currently the Director of the International Association of Earthquake Engineering. Roberto Nascimbene, PhD, is an Associate Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at the University of Pavia, Italy, in the Department of Civil Engineering and Architecture. He is also a National Committee Member of the European UNI/CT 021/SC 03 “Steel Structures” and a member of the Project Team SC8.T5 - Evolution of EN 1998-4 and EN 1998-6 “M/515 Phase 3 or 4.”

• Preface xiAcknowledgments xiiiIntroduction xv1 Appealing shell structures 11.1 Beams and arches . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Plates and vaults . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Rectangular and cylindrical tanks . . . . . . . . . . . . . . . . . . 121.4 Seismic behaviour of tanks . . . . . . . . . . . . . . . . . . . . . 231.5 Field observation of damage to tanks induced by seismic events 381.6 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . 481.7 A simplified description of seismic response of tanks . . . . . . . 571.8 Discussion on existing codes . . . . . . . . . . . . . . . . . . . . . 601.9 Content of the book . . . . . . . . . . . . . . . . . . . . . . . . . 662 Above ground anchored rigid tanks 672.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.2 Circular vertical anchored tanks . . . . . . . . . . . . . . . . . . . 682.2.1 Impulsive pressure component . . . . . . . . . . . . . 712.2.2 Convective pressure component . . . . . . . . . . . . 812.2.3 Effects of vertical component of the seismic action . 89vii2.2.4 Effects of tank inertia . . . . . . . . . . . . . . . . . . 922.2.5 Periods of vibration . . . . . . . . . . . . . . . . . . . 932.2.6 Effects of liquid viscosity . . . . . . . . . . . . . . . . 992.2.7 Effects of inhomogeneous liquids . . . . . . . . . . . 1022.2.8 Convective wave displacement and pressure . . . . . 1112.2.9 Combination of pressures and behavior factor . . . . 1182.2.10 Tank forces and stresses . . . . . . . . . . . . . . . . 1242.2.11 Effects of rocking motion . . . . . . . . . . . . . . . . 1312.3 Rectangular anchored tanks . . . . . . . . . . . . . . . . . . . . . 1362.3.1 Impulsive and convective pressure components . . . 1362.3.2 Periods of vibration . . . . . . . . . . . . . . . . . . . 1412.3.3 Convective wave displacement . . . . . . . . . . . . . 1432.3.4 Tank forces and stresses . . . . . . . . . . . . . . . . 1433 Above ground unanchored rigid tanks 1493.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.2 Vertical cylindrical tanks . . . . . . . . . . . . . . . . . . . . . . . 1533.2.1 Axial membrane stress in shell wall . . . . . . . . . . 1613.2.2 Shell uplift . . . . . . . . . . . . . . . . . . . . . . . . 1653.2.3 Radial membrane stress at base . . . . . . . . . . . . 1673.2.4 Plastic rotation at base . . . . . . . . . . . . . . . . . 1683.3 Rectangular tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1704 Elevated tanks 175viii4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1754.2 Single lumped-mass model . . . . . . . . . . . . . . . . . . . . . . 1824.3 Two uncoupled mass model . . . . . . . . . . . . . . . . . . . . . 1864.4 Two coupled masses model . . . . . . . . . . . . . . . . . . . . . 1905 Flexible tanks 2015.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2015.2 Impulsive pressure component . . . . . . . . . . . . . . . . . . . . 2055.2.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2055.2.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2195.3 Effects of vertical component of the seismic action . . . . . . . 2265.4 Periods of vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 2315.5 Combination of pressures . . . . . . . . . . . . . . . . . . . . . . 2465.6 Tank forces and stresses . . . . . . . . . . . . . . . . . . . . . . . 2555.6.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2575.6.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2705.7 Effects of rocking motion . . . . . . . . . . . . . . . . . . . . . . 2726 Other peculiar principles 2776.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2776.2 Effects of soil–structure interaction . . . . . . . . . . . . . . . . . 2786.3 Flow-dampening devices . . . . . . . . . . . . . . . . . . . . . . . 2886.4 Base-isolation devices . . . . . . . . . . . . . . . . . . . . . . . . 3026.5 Underground rigid tanks . . . . . . . . . . . . . . . . . . . . . . . 313ix6.6 Horizontal tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3176.7 Conical tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3247 General design principles 3337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3337.2 Requirements for steel tanks . . . . . . . . . . . . . . . . . . . . 3347.2.1 Base plate . . . . . . . . . . . . . . . . . . . . . . . . 3357.2.2 Sidewall . . . . . . . . . . . . . . . . . . . . . . . . . . 3397.2.3 Openings . . . . . . . . . . . . . . . . . . . . . . . . . 3487.2.4 Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3537.2.5 Foundation . . . . . . . . . . . . . . . . . . . . . . . . 3627.2.6 Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . 3737.2.7 Buckling limit state . . . . . . . . . . . . . . . . . . . 4067.3 Requirements for concrete tanks . . . . . . . . . . . . . . . . . . 4237.3.1 Serviceability limit state . . . . . . . . . . . . . . . . 4257.3.2 Ultimate limit state . . . . . . . . . . . . . . . . . . . 4357.3.3 Detailing and particular rules . . . . . . . . . . . . . . 436A Dimensionless design charts 463A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463B Codes, Manuals, Recommendations, Guidelines, Reports 471B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Gian Michele Calvi, PhD, is a Full Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at North Carolina State University, USA, in the Department of Civil, Construction, and Environmental Engineering. He is also the founder of the EUCENTRE Foundation for Training and Research in Earthquake Engineering and is currently the Director of the International Association of Earthquake Engineering. Roberto Nascimbene, PhD, is an Associate Professor of Structural Engineering at the IUSS Pavia, Italy, and Adjunct Professor at the University of Pavia, Italy, in the Department of Civil Engineering and Architecture. He is also a National Committee Member of the European UNI/CT 021/SC 03 “Steel Structures” and a member of the Project Team SC8.T5 - Evolution of EN 1998-4 and EN 1998-6 “M/515 Phase 3 or 4.”

• Preface xiAcknowledgments xiiiIntroduction xv1 Appealing shell structures 11.1 Beams and arches . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Plates and vaults . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Rectangular and cylindrical tanks . . . . . . . . . . . . . . . . . . 121.4 Seismic behaviour of tanks . . . . . . . . . . . . . . . . . . . . . 231.5 Field observation of damage to tanks induced by seismic events 381.6 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . 481.7 A simplified description of seismic response of tanks . . . . . . . 571.8 Discussion on existing codes . . . . . . . . . . . . . . . . . . . . . 601.9 Content of the book . . . . . . . . . . . . . . . . . . . . . . . . . 662 Above ground anchored rigid tanks 672.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.2 Circular vertical anchored tanks . . . . . . . . . . . . . . . . . . . 682.2.1 Impulsive pressure component . . . . . . . . . . . . . 712.2.2 Convective pressure component . . . . . . . . . . . . 812.2.3 Effects of vertical component of the seismic action . 89vii2.2.4 Effects of tank inertia . . . . . . . . . . . . . . . . . . 922.2.5 Periods of vibration . . . . . . . . . . . . . . . . . . . 932.2.6 Effects of liquid viscosity . . . . . . . . . . . . . . . . 992.2.7 Effects of inhomogeneous liquids . . . . . . . . . . . 1022.2.8 Convective wave displacement and pressure . . . . . 1112.2.9 Combination of pressures and behavior factor . . . . 1182.2.10 Tank forces and stresses . . . . . . . . . . . . . . . . 1242.2.11 Effects of rocking motion . . . . . . . . . . . . . . . . 1312.3 Rectangular anchored tanks . . . . . . . . . . . . . . . . . . . . . 1362.3.1 Impulsive and convective pressure components . . . 1362.3.2 Periods of vibration . . . . . . . . . . . . . . . . . . . 1412.3.3 Convective wave displacement . . . . . . . . . . . . . 1432.3.4 Tank forces and stresses . . . . . . . . . . . . . . . . 1433 Above ground unanchored rigid tanks 1493.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.2 Vertical cylindrical tanks . . . . . . . . . . . . . . . . . . . . . . . 1533.2.1 Axial membrane stress in shell wall . . . . . . . . . . 1613.2.2 Shell uplift . . . . . . . . . . . . . . . . . . . . . . . . 1653.2.3 Radial membrane stress at base . . . . . . . . . . . . 1673.2.4 Plastic rotation at base . . . . . . . . . . . . . . . . . 1683.3 Rectangular tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1704 Elevated tanks 175viii4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1754.2 Single lumped-mass model . . . . . . . . . . . . . . . . . . . . . . 1824.3 Two uncoupled mass model . . . . . . . . . . . . . . . . . . . . . 1864.4 Two coupled masses model . . . . . . . . . . . . . . . . . . . . . 1905 Flexible tanks 2015.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2015.2 Impulsive pressure component . . . . . . . . . . . . . . . . . . . . 2055.2.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2055.2.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2195.3 Effects of vertical component of the seismic action . . . . . . . 2265.4 Periods of vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 2315.5 Combination of pressures . . . . . . . . . . . . . . . . . . . . . . 2465.6 Tank forces and stresses . . . . . . . . . . . . . . . . . . . . . . . 2555.6.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 2575.6.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 2705.7 Effects of rocking motion . . . . . . . . . . . . . . . . . . . . . . 2726 Other peculiar principles 2776.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2776.2 Effects of soil–structure interaction . . . . . . . . . . . . . . . . . 2786.3 Flow-dampening devices . . . . . . . . . . . . . . . . . . . . . . . 2886.4 Base-isolation devices . . . . . . . . . . . . . . . . . . . . . . . . 3026.5 Underground rigid tanks . . . . . . . . . . . . . . . . . . . . . . . 313ix6.6 Horizontal tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3176.7 Conical tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3247 General design principles 3337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3337.2 Requirements for steel tanks . . . . . . . . . . . . . . . . . . . . 3347.2.1 Base plate . . . . . . . . . . . . . . . . . . . . . . . . 3357.2.2 Sidewall . . . . . . . . . . . . . . . . . . . . . . . . . . 3397.2.3 Openings . . . . . . . . . . . . . . . . . . . . . . . . . 3487.2.4 Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3537.2.5 Foundation . . . . . . . . . . . . . . . . . . . . . . . . 3627.2.6 Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . 3737.2.7 Buckling limit state . . . . . . . . . . . . . . . . . . . 4067.3 Requirements for concrete tanks . . . . . . . . . . . . . . . . . . 4237.3.1 Serviceability limit state . . . . . . . . . . . . . . . . 4257.3.2 Ultimate limit state . . . . . . . . . . . . . . . . . . . 4357.3.3 Detailing and particular rules . . . . . . . . . . . . . . 436A Dimensionless design charts 463A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463B Codes, Manuals, Recommendations, Guidelines, Reports 471B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486